Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 07 Jul 2015, 10:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the least number which, when divided by 52, leaves

Author Message
TAGS:
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 719 [0], given: 781

What is the least number which, when divided by 52, leaves [#permalink]  20 Sep 2003, 12:27
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
What is the least number which, when divided by 52, leaves the
remainder 33, and when divided by 78, leaves 59, and when divided by
117 leaves 98 as the respective remainders?

What can be said about a clock when the two hands of the clock
coincide every 65 minutes?

(A) It gains time
(B) It loses time
(C) Shows the correct time
(D) Data insufficient
(E) Loses and gains time alternatively
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
Followers: 1

Kudos [?]: 4 [0], given: 0

For second question:
My asnwer: B (loses time).
first - under study..
-vicks
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 719 [0], given: 781

Vicky wrote:
For second question:
My asnwer: B (loses time).
first - under study..
-vicks

Its time you get B under study too

Try again on B
Intern
Joined: 12 Sep 2003
Posts: 31
Location: Peru
Followers: 0

Kudos [?]: 0 [0], given: 0

2- Gains time?

In 65 minutes the minute hand should move a 1+(1/12) rounds, this is five "places" from its original. The hour hand should moves five "places" and a little bit more every 65 minutes. So, if they coincide every 65 minutes the minute hand is moving faster than it should, so, it is gaining time.
Intern
Joined: 16 Jul 2003
Posts: 32
Followers: 0

Kudos [?]: 0 [0], given: 0

My approach - Let number be X.

So X= 52N+33=78M+59=117P+98, where M,N, P are divisors(?? I guess).

We know that the smallest number which can be divided by 52, 78 and 117 is 13x2x2x3x3 = 52x9 = 468.

Now, look at the remainders in each case, I can write 33 as (52-19), 59 as 78-19, and 98 as 117-19. Did you find a pattern. yes.

Now rewrite the equation.

X = 52(N+1) - 19 = 78(M+1) - 19 and 117(P+1) - 19.

So now, the ques. boils down to find GCD of 52,78,and 117 ( which we know = 468 ) and deduct 19 from it = 449.

Just to test the answer 449 / 52 = 9 + 33 remainder.

449/78 = 5 + 59 remainder, and 449/117 = 3 + 98 remainder.

2. A. It gains time. Instead coinciding every 65+5/11 mins. hands coincide every 65 mins.

so gain of 5/11 every 65 mins.
Similar topics Replies Last post
Similar
Topics:
9 A number when divided successively by 4 and 5 leaves 9 28 Aug 2012, 21:32
13 A number when divided by 36 leaves a reminder of 23. Which o 9 24 Nov 2011, 09:37
25 A number when divided by a divisor leaves a remainder of 24. 26 07 Apr 2007, 22:45
Two numbers when divided by a certain divisor leave 4 31 Oct 2005, 23:43
Display posts from previous: Sort by